Allometric power-law relationships in a Hortonian fractal digital elevation model

• Published in: Geophysical research letters Vol. 31; no. 6; pp. L06501 - n/a
• Main Authors: Sagar, B. S. Daya, Tien, Tay Lea
• Format: Journal Article
• Language: English
• Published: American Geophysical Union 01-03-2004; Blackwell Publishing Ltd
• Subjects: Fractals and multifractals; Geomorphology; Hydrology; Mathematical Geophysics; Modeling; Networks
• ISSN: 0094-8276; 1944-8007
• DOI: 10.1029/2003GL019093

We provide a topologically viable model that is geomorphologically realistic from the point of its Hortonity and general allometric scaling laws. To illustrate this, we consider a fractal binary basin, generated in such a way that it follows certain postulates, and decompose it into various coded topologically prominent regions the union of which is defined as geomorphologically realistic Fractal‐DEM. We derive two unique topological networks from this Hortonian fractal DEM based on which we derive allometric power‐law relationships among the basic measures of decomposed sub‐basins of all orders ranging from ω = 1 to ω = Ω. Our results are in good accord with optimal channel networks and natural river basins.